Find the equation of the circle with centre (0, 2) and radius 2
The equation of a circle with centre (h, k) and radius r is given as
(x – h)2 + (y – k)2 = r2
It is given that centre (h, k) = (0, 2) and radius (r) = 2.
Therefore, the equation of the circle is
(x – 0)2 + (y – 2)2 = 22
x2 + y2 + 4 – 4 y = 4
x2 + y2 – 4y = 0
Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer.
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
A point is on the x-axis. What are its y-coordinates and z-coordinates?
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
Describe the sample space for the indicated experiment: A coin is tossed three times.
Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
A point is in the XZ-plane. What can you say about its y-coordinate?
Describe the sample space for the indicated experiment: A die is thrown two times.
Find the sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32 + …
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
For what values of x, the numbers are in G.P?
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
Prove the following by using the principle of mathematical induction for all n ∈ N:
n (n + 1) (n + 5) is a multiple of 3.